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Yes, a monomial can be a quadratic polynomial. A polynomial of degree two is called a quadratic polynomial. A quadratic polynomial might be a monomial, a binomial or a trinomial. A polynomial is any sum (or difference) of terms, and monomials, binomials, and trinomials are also polynomials. The term "polynomial" refers generally to any of these.
Yes, a monomial can be a quadratic function.
Quadratic functions
The major characterization criteria for a quadratic function is that it's highest order be 2.
A polynomial can be classified based on the number of terms it contains as either a monomial, binomial, trinomial or as the case may be.
On this note, it follows that a quadratic equation may be a monomial.
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